Observation: Organisms have parts which can be measured in terms of length. Suppose you previously made some measurements on yourself. With those measurements in mind, you would now have a "human ruler." You could measure a centimeter at a time with one of your fingernails, and could measure longer lengths by "walking" with your thumb and index finger.

Observation: You now know something about your own two hands. You also notice that not everyone in the room is the same size overall.

Question: In spite of different absolute body sizes, does everyone have hands of equal width?

Hypothesis: The human population has hands of equal width.

Prediction: If the human population has hands of equal width, then a sample of the human population should have hands of equal width.

Notice that we cannot go out and measure the hands of the entire human population, so we must settle for a sample. We hope we can take a representative sample (that is a random sample). Our sample will be all the people in this laboratory.

We also hope that our sample is sufficiently large. In spite of any shortcomings in our sample, we will continue our analysis since we lack a better sample.

Experiment: Your instructor will help you post your hand width data along with your classmates' on the blackboard.

Analysis: Clearly we have various widths in each sample and must now include an assessment of this variation in preparing for our decision. Calculate the mean (average) width and the standard deviation of the samples. The latter gives us some measure of the variation (or spread) around the mean. Most calculators will determine the mean and standard deviation using the formulae shown below for you, but we will let a computer do this work for us!

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We will let a computer determine the t-statistic for our samples. The formula it is using assumes n₁=n₂.

Ignore any negative sign carried by the t-statistic.

This t-statistic is compared with a value in a t-table.

The table value is found by using a row defined by the degrees of freedom:

and a column defined by the acceptable level of error. As scientists, what level of error is acceptable? Most scientists admit that 5% of the time chance alone will explain errors. Our table includes a 5% column.

Circle the pertinent table value in the table → → →

Decision Rules:

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Observations: A single bag of beans was purchased from the store. Some of the beans were soaked in water overnight, the rest from the same bag remain dry. Clearly the soaking has had some effect upon length.

Question: Does soaking beans cause them to expand?

Hypothesis: Soaking causes beans to expand.

Prediction: If soaking causes beans to expand, then beans will be significantly larger when they are soaked than beans which have been kept dry.

Experiment: A sample of beans was divided into two sub-samples. One sub-sample was placed in water, the other sub-sample was kept in dry conditions. Use a balance to its greatest precision to determine the weight of each of 10 beans from each sub-sample.

Analysis: Carry out a t-test to see whether there is any significant difference between the two sub-samples.

Decision:

Our hypothesis used the term "expand" and our prediction used the term "larger." In our experiment we tested the weight of the soaked beans.

This page © Ross E. Koning 1994.

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